The crawler combine harvester fits better in paddy soil farmland because of its much smaller pressure between the ground and track than that of wheeled vehicle. However, the existing unilateral brake steering mode in crawler combine harvester has led to inflexibility and caused many problems. This paper developed a differential steering gearbox (DSG) that could realize any turning radius in the form of dual hydraulic static transmission (HST) combining with a mechanical gearbox. The mathematical relationship of all motion states was deduced. The principle of the DSG was analyzed by using virtual prototype simulation software RecurDyn, as well as dynamic performance under three different working modes of dual HST. The size of the turning radius is only relevant to the steering HST output speed but has nothing to do with the straight HST output speed. Experiment results showed that the error rates of the transmission ratios of the straight (low, middle, and high speed) and steering routes were 0.1%, 0.8%, 0.5%, 0.8% respectively, which well verifies the developed DSG model and principle. This research can provide theoretical basis for optimal design and data support for electronic control of the gearbox.